318_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

318_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.8.qxd 9/27/08 312 1:13 PM Page 312 CHAPTER 3 Torsion BRASS CORE (ONLY) Ta Eq. (3-44b): TS GSIPS b GBIPB + GSIPS 0.762082 T T TB TS (CHECK) ALLOWABLE TORQUE T BASED UPON BRASS CORE p4 d 32 1 IPB 251.327 * 10 9 TB(d1/2) 2tBIPB TB IPB d1 Substitute numerical values: m4 tB 9047.79 N m2 GBIPB TB STEEL SLEEVE (ONLY) 0.237918 T 2(48 MPa)(251.327 * 10 40 mm T 9 m4) 2535 N m ALLOWABLE TORQUE T BASED UPON STEEL SLEEVE IPS GSIPS p4 (d 32 2 4 d1) 362.265 * 10 9 m4 2 28,981.2 N m tS Eq. (3-44a): TB TB Ta TS 2tSIPS d2 0.762082 T 2(80 MPa)(362.265 * 10 50 mm TS GBIPB b GBIPB + GS IPS TS SUBSTITUTE NUMERICAL VALUES: TORQUES Total torque: T TS(d2/2) IPS T 9 m4) 1521 N m STEEL SLEEVE GOVERNS Tmax 1520 N m ; 0.237918 T Problem 3.8-13 The composite shaft shown in the figure is manufactured by shrink-fitting a steel sleeve over a brass core so that the two parts act as a single solid bar in torsion. The outer diameters of the two parts are d1 1.6 in. for the brass core and d2 2.0 in. for the steel sleeve. The shear moduli of elasticity are Gb 5400 ksi for the brass and Gs 12,000 ksi for the steel. Assuming that the allowable shear stresses in the brass and steel are b 4500 psi and s 7500 psi, respectively, determine the maximum permissible torque Tmax that may be applied to the shaft. (Hint: Use Eqs. 3-44a and b to find the torques.) ...
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